Advertisement

Journal of Computational Neuroscience

, Volume 45, Issue 1, pp 29–43 | Cite as

A model of motor and sensory axon activation in the median nerve using surface electrical stimulation

  • Jessica L. Gaines
  • Kathleen E. Finn
  • Julia P. Slopsema
  • Lane A. Heyboer
  • Katharine H. Polasek
Article
  • 293 Downloads

Abstract

Surface electrical stimulation has the potential to be a powerful and non-invasive treatment for a variety of medical conditions but currently it is difficult to obtain consistent evoked responses. A viable clinical system must be able to adapt to variations in individuals to produce repeatable results. To more fully study the effect of these variations without performing exhaustive testing on human subjects, a system of computer models was created to predict motor and sensory axon activation in the median nerve due to surface electrical stimulation at the elbow. An anatomically-based finite element model of the arm was built to accurately predict voltages resulting from surface electrical stimulation. In addition, two axon models were developed based on previously published models to incorporate physiological differences between sensory and motor axons. This resulted in axon models that could reproduce experimental results for conduction velocity, strength-duration curves and activation threshold. Differences in experimentally obtained action potential shape between the motor and sensory axons were reflected in the models. The models predicted a lower threshold for sensory axons than motor axons of the same diameter, allowing a range of sensory axons to be activated before any motor axons. This system of models will be a useful tool for development of surface electrical stimulation as a method to target specific neural functions.

Keywords

Axon model Motor axon model Sensory axon model Finite element model Surface electrical stimulation 

Notes

Acknowledgments

The authors would like to express appreciation to Matthew Schiefer for his assistance in using Ansys and general modeling advice.

Funding

Funding was received from the following entities but none of these entities had any role in design of the study or analysis of the data.

• Hope College Dean of Natural and Applied Sciences.

• A grant to ‘Hope College’ from the Howard Hughes Medical Institute through the Precollege and Undergraduate Science Education Program.

• Michigan Space Grant Consortium Undergraduate Fellowship Program.

• Hope College Nyenhuis Faculty Development Fund.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest

References

  1. Angeli, C. A., Edgerton, V. R., Gerasimenko, Y. P., & Harkema, S. J. (2014). Altering spinal cord excitability enables voluntary movements after chronic complete paralysis in humans. Brain, 137(Pt 5), 1394–1409.  https://doi.org/10.1093/brain/awu038awu038.CrossRefPubMedPubMedCentralGoogle Scholar
  2. Birmingham, K., Gradinaru, V., Anikeeva, P., Grill, W. M., Pikov, V., McLaughlin, B., Pasricha, P., Weber, D., Ludwig, K., & Famm, K. (2014). Bioelectronic medicines: A research roadmap. Nature Reviews. Drug Discovery, 13(6), 399–400.  https://doi.org/10.1038/nrd4351nrd4351.CrossRefPubMedGoogle Scholar
  3. Bostock, H., & Rothwell, J. C. (1997). Latent addition in motor and sensory fibres of human peripheral nerve. J Physiol, 498(Pt 1), 277–294. http://www.ncbi.nlm.nih.gov/pubmed/9023784
  4. Bostock, H., Baker, M., & Reid, G. (1991). Changes in excitability of human motor axons underlying post-ischaemic fasciculations: Evidence for two stable states. The Journal of Physiology, 441, 537–557. http://www.ncbi.nlm.nih.gov/pubmed/1667800
  5. Boyd, I. A., & Davey, M. R. (1968). Composition of peripheral nerves. Edinburgh: E. & S. Livingstone.Google Scholar
  6. Boyd, I. A., & Kalu, K. U. (1979). Scaling factor relating conduction velocity and diameter for myelinated afferent nerve fibres in the cat hind limb. The Journal of Physiology, 289, 277–297.  https://doi.org/10.1113/jphysiol.1979.sp012737.CrossRefPubMedPubMedCentralGoogle Scholar
  7. Buchthal, F., & Rosenfalck, A. (1966). Number and diameter of myelinated fibres in human sensory nerves. Brain Research, 3(1), 85–94.CrossRefGoogle Scholar
  8. Choi, A. Q., Cavanaugh, J. K., & Durand, D. M. (2001). Selectivity of multiple-contact nerve cuff electrodes: A simulation analysis. IEEE Transactions on Biomedical Engineering, 48(2), 165–172.  https://doi.org/10.1109/10.909637.CrossRefPubMedGoogle Scholar
  9. David, G., Modney, B., Scappaticci, K. A., Barrett, J. N., & Barrett, E. F. (1995). Electrical and morphological factors influencing the depolarizing after-potential in rat and lizard myelinated axons. J Physiol, 489(Pt 1), 141–157. http://www.ncbi.nlm.nih.gov/pubmed/8583398
  10. Dawson, G. D. (1956). The relative excitability and conduction velocity of sensory and motor nerve fibres in man. The Journal of Physiology, 131(2), 436–451. http://www.ncbi.nlm.nih.gov/pubmed/13320345
  11. Dimbylow, P. J. (2000). Electromagnetic field calculations in an anatomically realistic voxel model of the human body. In B. J. Klauenberg & D. Miklavcic (Eds.), Radio Frequency Radiation Dosimetry and its Relationship to the Biological Effects of Electromagnetic Fields (p. 127). Dordrecht: Kluwer Academic Publishers.Google Scholar
  12. Dorgan, S. J., & Reilly, R. B. (1999). A model for human skin impedance during surface functional neuromuscular stimulation. IEEE Transactions on Rehabilitation Engineering, 7(3), 341–348. http://www.ncbi.nlm.nih.gov/pubmed/10498379
  13. Drillis, R., Contini, R., & Bluestein, M. (1964). Body segment parameters; a survey of measurement techniques. Artificial Limbs, 8, 44–66. http://www.ncbi.nlm.nih.gov/pubmed/14208177
  14. Elbow Cross Sectional Anatomy. (2014). Electronic Open Reduction Internal Fixation Reference. http://www.eorif.com/elbow-cross-sectional-anatomy
  15. Erlanger, J., & Blair, E. A. (1938). Comparative observations on motor and sensory fibers with special reference to repetitiousness. American Journal of Physiology, 121, 431–453.Google Scholar
  16. Feinstein, B., Lindegard, B., Nyman, E., & Wohlfart, G. (1955). Morphologic studies of motor units in normal human muscles. Acta Anatomica (Basel), 23(2), 127–142. http://www.ncbi.nlm.nih.gov/pubmed/14349537
  17. Forst, J. C., Blok, D. C., Slopsema, J. P., Boss, J. M., Heyboer, L. A., Tobias, C. M., & Polasek, K. H. (2015). Surface electrical stimulation to evoke referred sensation. Journal of Rehabilitation Research and Development, 52(4), 397–406.CrossRefPubMedGoogle Scholar
  18. Geddes, L. A., & Baker, L. E. (1967). The specific resistance of biological material--a compendium of data for the biomedical engineer and physiologist. Medical & Biological Engineering, 5(3), 271–293. http://www.ncbi.nlm.nih.gov/pubmed/6068939
  19. Goffredo, M., Schmid, M., Conforto, S., Bilotti, F., Palma, C., Vegni, L., & D’Alessio, T. (2014). A two-step model to optimise transcutaneous electrical stimulation of the human upper arm. Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 33(4), 1329–1345.  https://doi.org/10.1108/Compel-04-2013-0118.CrossRefGoogle Scholar
  20. Grill, W. M. (2004). Electrical stimulation of the peripheral nervous system: Biophysics and excitation properties. In K. W. Horch & K. Yoshida (Eds.), Neuroprosthetics: Theory and Practice (pp. 319–340). Singapore: World Scientific Publishing Co.CrossRefGoogle Scholar
  21. Grill, W., & Mortimer, J. T. (1997). Inversion of the current-distance relationship by transient depolarization. IEEE Transactions on Biomedical Engineering, 44(1), 1–9. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=9214779
  22. Grinberg, Y., Schiefer, M. A., Tyler, D. J., & Gustafson, K. J. (2008). Fascicular perineurium thickness, size, and position affect model predictions of neural excitation. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 16(6), 572–581. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=19144589
  23. Hines, M. L., & Carnevale, N. T. (1997). The NEURON simulation environment. Neural Computation, 9(6), 1179–1209. http://www.ncbi.nlm.nih.gov/pubmed/9248061
  24. Howells, J., Trevillion, L., Bostock, H., & Burke, D. (2012). The voltage dependence of I(h) in human myelinated axons. The Journal of Physiology, 590(Pt 7), 1625–1640.  https://doi.org/10.1113/jphysiol.2011.225573.CrossRefPubMedPubMedCentralGoogle Scholar
  25. Keller, T., & Kuhn, A. (2008). Electrodes for transcutaneous (surface) electrical stimulation. Journal of Automatic Control, 18(2), 35–45.  https://doi.org/10.2298/JAC0802035K.CrossRefGoogle Scholar
  26. Kiernan, M. C., Mogyoros, I., & Burke, D. (1996). Differences in the recovery of excitability in sensory and motor axons of human median nerve. Brain, 119\(Pt 4), 1099–1105. http://www.ncbi.nlm.nih.gov/pubmed/8813274Google Scholar
  27. Kilgore, K. L., & Bhadra, N. (2004). Nerve conduction block utilising high-frequency alternating current. Medical & Biological Engineering & Computing, 42(3), 394–406. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15191086
  28. Kuhn, A., Keller, T., Lawrence, M., & Morari, M. (2009). A model for transcutaneous current stimulation: Simulations and experiments. Medical & Biological Engineering & Computing, 47(3), 279–289.  https://doi.org/10.1007/s11517-008-0422-z.CrossRefGoogle Scholar
  29. Kuhn, A., Keller, T., Lawrence, M., & Morari, M. (2010). The influence of electrode size on selectivity and comfort in transcutaneous electrical stimulation of the forearm. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 18(3), 255–262.  https://doi.org/10.1109/TNSRE.2009.2039807.CrossRefPubMedGoogle Scholar
  30. McIntyre, C. C., & Grill, W. M. (2002). Extracellular stimulation of central neurons : Influence of stimulus waveform and frequency on neuronal output. Journal of Neurophysiology, 88, 1592–1604.CrossRefPubMedGoogle Scholar
  31. McIntyre, C., Richardson, A. G., & Grill, W. M. (2002). Modeling the excitability of mammalian nerve fibers: Influence of afterpotentials on the recovery cycle. Journal of Neurophysiology, 87(2), 995–1006. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=11826063
  32. Medina, L. E., & Grill, W. M. (2016). Nerve excitation using an amplitude-modulated signal with kilohertz-frequency carrier and non-zero offset. Journal of NeuroEngineering and Rehabilitation, 13(1), 63.  https://doi.org/10.1186/s12984-016-0171-4.CrossRefPubMedPubMedCentralGoogle Scholar
  33. Miles, J. D., Kilgore, K. L., Bhadra, N., & Lahowetz, E. A. (2007). Effects of ramped amplitude waveforms on the onset response of high-frequency mammalian nerve block. Journal of Neural Engineering, 4(4), 390–398. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=18057506
  34. Mogyoros, I., Kiernan, M. C., & Burke, D. (1996). Strength-duration properties of human peripheral nerve. Brain, 119(Pt 2), 439–447. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=8800939
  35. Panescu, D., Webster, J. G., & Stratbucker, R. A. (1994). A nonlinear finite element model of the electrode-electrolyte-skin system. IEEE Transactions on Biomedical Engineering, 41(7), 681–687.CrossRefPubMedGoogle Scholar
  36. Panizza, M., Nilsson, J., Roth, B. J., Rothwell, J., & Hallett, M. (1994). The time constants of motor and sensory peripheral nerve fibers measured with the method of latent addition. Electroencephalography and Clinical Neurophysiology, 93(2), 147–154. http://www.ncbi.nlm.nih.gov/pubmed/7512921
  37. Peterson, E. J., Izad, O., & Tyler, D. J. (2011). Predicting myelinated axon activation using spatial characteristics of the extracellular field. Journal of Neural Engineering, 8(4), 46030.  https://doi.org/10.1088/1741-2560/8/4/046030.CrossRefGoogle Scholar
  38. Peurala, S. H., Pitkanen, K., Sivenius, J., & Tarkka, I. M. (2002). Cutaneous electrical stimulation may enhance sensorimotor recovery in chronic stroke. Clinical Rehabilitation, 16(7), 709–716 http://www.ncbi.nlm.nih.gov/pubmed/12428819.CrossRefPubMedGoogle Scholar
  39. Ranck, J. B., & BeMent, S. L. (1965). The specific impedance of the dorsal columns of cat: An anisotropic medium. Experimental Neurology, 11(4), 451–463.  https://doi.org/10.1016/0014-4886(65)90059-2.CrossRefPubMedGoogle Scholar
  40. Roper, J., & Schwarz, J. R. (1989). Heterogeneous distribution of fast and slow potassium channels in myelinated rat nerve fibres. The Journal of Physiology, 416, 93–110. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1189205/
  41. Schiefer, M. A., Triolo, R. J., & Tyler, D. J. (2008). A model of selective activation of the femoral nerve with a flat interface nerve electrode for a lower extremity neuroprosthesis. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 16(2), 195–204. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=18403289
  42. Sha, N., Kenney, L. P. J., Heller, B. W., Barker, A. T., Howard, D., & Moatamedi, M. (2008). A Finite Element Model to Identify Electrode Influence on Current Distribution in the Skin, 32(8), 639–643.  https://doi.org/10.1111/j.1525-1594.2008.00615.x.
  43. Stebbing, M. J., Eschenfelder, S., Habler, H. J., Acosta, M. C., Janig, W., & McLachlan, E. M. (1999). Changes in the action potential in sensory neurones after peripheral axotomy in vivo. Neuroreport, 10(2), 201–206.  https://doi.org/10.1097/00001756-199902050-00001.CrossRefPubMedGoogle Scholar
  44. Sunderland, S. (1978). Nerves and nerve injury (2nd ed.). New York: Churchill Livingstone.Google Scholar
  45. Suresh, S., Smith, L., & Tyler, D. J. (2006). Fascicular anatomy of upper extremity nerves for Neuroprosthesis development. Chicago: Biomedical Engineering Society.Google Scholar
  46. Veale, J. L., Mark, R. F., & Rees, S. (1973). Differential sensitivity of motor and sensory fibres in human ulnar nerve. Journal of Neurology, Neurosurgery, and Psychiatry, 36(1), 75–86. http://www.ncbi.nlm.nih.gov/pubmed/4348037
  47. Walker, E. R., Hyngstrom, A. S., & Schmit, B. D. (2014). Sensory electrical stimulation improves foot placement during targeted stepping post-stroke. Experimental Brain Research, 232, 1137–1143.  https://doi.org/10.1007/s00221-014-3823-2.CrossRefPubMedPubMedCentralGoogle Scholar
  48. Warman, E. N., Grill, W. M., & Durand, D. (1992). Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds. IEEE Transactions on Biomedical Engineering, 39(12), 1244–1254. http://www.ncbi.nlm.nih.gov/pubmed/1487287
  49. Weerasuriya, A., Spangler, R. A., Rapoport, S. I., & Taylor, R. E. (1984). AC impedance of the perineurium of the frog sciatic nerve. Biophysical Journal, 46(2), 167–174.  https://doi.org/10.1016/S0006-3495(84)84009-6.CrossRefPubMedPubMedCentralGoogle Scholar
  50. Wesselink, W. A., Holsheimer, J., & Boom, H. B. (1999). A model of the electrical behaviour of myelinated sensory nerve fibres based on human data. Medical & Biological Engineering & Computing, 37(2), 228–235. http://www.ncbi.nlm.nih.gov/pubmed/10396827
  51. Wongsarnpigoon, A., Woock, J. P., & Grill, W. M. (2010). Efficiency analysis of waveform shape for electrical excitation of nerve fibers. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 18(3), 319–328.  https://doi.org/10.1109/TNSRE.2010.2047610.CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hope CollegeHollandUSA
  2. 2.University of MinnesotaMinneapolisUSA

Personalised recommendations